{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Random Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Random signals are signals whose values are not (or only to a limited extend) predictable. Frequently used alternative terms are\n",
    "\n",
    "* stochastic signals\n",
    "* non-deterministic signals\n",
    "\n",
    "Random signals play an important role in various fields of signal processing and communications. This is due to the fact that only random signals carry information. A signal which is observed by a receiver has to be unknown to some degree in order to represent novel [information](https://en.wikipedia.org/wiki/Information).\n",
    "\n",
    "Random signals are often classified as useful/desired and disturbing/interfering signals. For instance\n",
    "\n",
    "* useful signals: data, speech, music, images, ...\n",
    "* disturbing signals: thermal noise at a resistor, amplifier noise, quantization noise, cosmic microwave background...\n",
    "\n",
    "Practical signals are frequently modeled as a combination of useful signals and additive noise.\n",
    "\n",
    "As the values of a random signal cannot be foreseen, the properties of random signals are described by the their statistical characteristics. One measure is for instance the average value of a random signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Random Signals**\n",
    "\n",
    "The following audio examples illustrate the characteristics of some deterministic and random signals. Lower the volume of your headphones or loudspeakers before playing back the examples.\n",
    "\n",
    "1. Cosine signal\n",
    "\n",
    "    <audio src=\"./cosine.wav\" controls>Your browser does not support the audio element.</audio>[./cosine.wav](./cosine.wav)\n",
    "2. Noise\n",
    "\n",
    "    <audio src=\"./noise.wav\" controls>Your browser does not support the audio element.</audio>[./noise.wav](./noise.wav)\n",
    "3. Cosine signal superpositioned by noise\n",
    "\n",
    "    <audio src=\"./cosine_noise.wav\" controls>Your browser does not support the audio element.</audio>[./cosine_noise.wav](./cosine_noise.wav)\n",
    "4. Speech signal\n",
    "\n",
    "    <audio src=\"../data/speech.wav\" controls>Your browser does not support the audio element.</audio>[../data/speech.wav](../data/speech.wav)\n",
    "5. Speech signal superpositioned by noise\n",
    "\n",
    "    <audio src=\"./speech_noise.wav\" controls>Your browser does not support the audio element.</audio>[./speech_noise.wav](./speech_noise.wav)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Excercise**\n",
    "\n",
    "* Which example can be considered as deterministic, random signal or combination of both?\n",
    "\n",
    "Solution: The cosine signal is the only deterministic signal. Noise and speech are random signals, as their samples can not (or only to a limited extend) be predicted from previous samples. The superposition of the cosine and noise signals is a combination of a deterministic and a random signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Processing of Random Signals\n",
    "\n",
    "In contrary to the assumption of deterministic signals in traditional signal processing, [statistical signal processing](https://en.wikipedia.org/wiki/Statistical_signal_processing) treats signals explicitly as random signals. Two prominent application examples involving random signals are:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Measurement of physical quantities\n",
    "\n",
    "The measurement of physical quantities is often subject to additive noise and distortions. The additive noise models e.g. the sensor noise. The distortions, by e.g. the transmission properties of an amplifier, may be modeled by a system.\n",
    "\n",
    "![Model for the measurement of physical quantities](measurement_channel.png)\n",
    "\n",
    "$\\mathcal{H}$ denotes an arbitrary (not necessarily LTI) system. The aim of statistical signal processing is to estimate the physical quantity from the observed sensor data, given some knowledge on the disturbing system and the statistical properties of the noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Communication channel\n",
    "\n",
    "In communications engineering a message is sent over a channel that distorts the signal by e.g. multipath propagation. Additive noise is present at the receiver due to background and amplifier noise.\n",
    "\n",
    "![Model for the transmission of a message over a communication channel](communication_channel.png)\n",
    "\n",
    "The aim of statistical signal processing is to estimate the sent message from the received message, given some knowledge on the disturbing system and the statistical properties of the noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Processes\n",
    "\n",
    "A random process is a [stochastic process](https://en.wikipedia.org/wiki/Stochastic_process) which generates an ensemble of random signals. A random process\n",
    "\n",
    "* provides a mathematical model for an ensemble of random signals and\n",
    "* generates different sample functions with specific common properties.\n",
    "\n",
    "It is important to differentiate between an\n",
    "\n",
    "* *ensemble*: collection of all possible signals of a random process and an\n",
    "* *sample function*: one specific random signal.\n",
    "\n",
    "An example for a random process is speech produced by humans. Here the ensemble is composed from the speech signals produced by all humans on earth, one particular speech signal produced by one person at a specific time is a sample function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example - Sample functions of a random process**\n",
    "\n",
    "The following example shows sample functions of a continuous amplitude real-valued random process. All sample functions have the same properties with respect to certain statistical measures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1000x1200 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 5  # number of sample functions\n",
    "\n",
    "# draw N sample functions from a random process\n",
    "np.random.seed(0)\n",
    "x = np.random.normal(size=(N, 32))\n",
    "\n",
    "# plot sample functions\n",
    "fig = plt.figure(figsize=(10, 12))\n",
    "for n in range(N):\n",
    "    plt.subplot(N, 1, n + 1)\n",
    "    plt.tight_layout()\n",
    "    plt.stem(x[n, :], basefmt=\"C0:\")\n",
    "    plt.title(\"Sample Function %d\" % n)\n",
    "    plt.xlabel(r\"$k$\")\n",
    "    plt.ylabel(r\"$x_%d[k]$\" % n)\n",
    "    plt.axis([-1, 32, -3, 3])\n",
    "    plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* What is different, what is common between the sample functions?\n",
    "\n",
    "Solution: You may have observed that the amplitude values of the individual sample functions $x_n[k]$ differ for a fixed time instant $k$. However, the sample functions seem to share some common properties. For instance, positive and negative values seem to occur with approximately the same probability. Furthermore, positive and negative values seem to be aligned around zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties of Random Processes and Random Signals\n",
    "\n",
    "It was already argued above, that it is not meaningful to describe a random signal by the amplitude values of a particular sample function. Instead, random signals are characterized by specific statistical measures. In statistical signal processing it is common to use\n",
    "\n",
    "* amplitude distributions and\n",
    "* ensemble averages/moments\n",
    "\n",
    "for this purpose. These measures will be introduced in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
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 },
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